I don't think your definitions are quite accurate. Terrorism is "the calculated use of violence to create a general climate of fear in a population and thereby to bring about a particular political objective." This is distinct from assassination, resistance fighting, and war, although I would argue the campaigns sold to the public as war are usually large-scale terrorism in practice.

Isolation, hate, and fear certainly do drive some vulnerable people to extreme actions, but I think the term "terrorism" is overused by people with a political agenda and political enemies.